Prime p₀= 2509214400554279027 starts a Tuple of 14 consecutive primes, which form 7 twin primes (TPT).
d_n: 0 2 22 2 4 2 10 2 118 2 28 2 16 2 (?)
a_n: 0 2 24 26 30 32 42 44 162 164 192 194 210 212
All 14 integers p_n = p₀+a_n = p_n-1+d_n are prime and there are no other primes in the gaps.
diameter: 212
Found by: [SG-FC] hl
db: batch=82, k=14, 22 4 10 118 28 16

SPT(16)	2509213428845337761	0 56 72 78 126 140 176 182 186 192 228 242 290 296 312 368	-971708941266
SPT(16)	2509213679351003423	0 14 78 80 108 138 156 198 206 248 266 296 324 326 390 404	-721203275604
SPT(16)	2509213971335275409	0 18 62 78 80 128 132 150 182 200 204 252 254 270 314 332	-429219003618
SPT(16)	2509213996488113653	0 40 46 78 84 90 96 120 124 148 154 160 166 198 204 244	-404066165374
SPT(16)	2509214383669985681	0 26 30 56 78 110 140 152 186 198 228 260 282 308 312 338	-16884293346
SPT(16)	2509214394650170261	0 42 66 82 118 216 220 270 328 378 382 480 516 532 556 598	-5904108766
SPT(16)	2509214411387523083	0 14 24 30 90 140 156 210 254 308 324 374 434 440 450 464	10833244056
TPT(14)	2509214805376969847	0 2 24 26 42 44 174 176 180 182 222 224 300 302	404822690820
STPT(10)	2509214815145495069	0 2 18 20 30 32 42 44 60 62	414591216042
STPT(10)	2509215470423566547	0 2 24 26 42 44 60 62 84 86	1069869287520
SPT(16)	2509215796906656679	0 4 10 18 24 142 154 178 204 228 240 358 364 372 378 382	1396352377652